Phasor Diagram of Synchronous Generator

Phasor Diagram Defined

A phasor diagram is a graphical representation of the phase relationships between different electrical quantities in an AC circuit, specifically used here for synchronous generators.

Drawing Basics

Ef which denotes excitation voltage

Vt which denotes terminal voltage

Ia which denotes the armature current

θ which denotes the phase angle between Vt and Ia

ᴪ which denotes the angle between the Ef and Ia

δ which denotes the angle between the Ef and Vt

ra which denotes the armature per phase resistance

 Phasor Relationships

In the diagram, the phasor for excitation voltage (Ef) is always ahead of the terminal voltage (Vt), crucial for understanding generator operations.

Operational Conditions

The phasor diagrams vary with operational conditions—lagging, unity, and leading power factors—each affecting the voltage and current relationships differently.

 Phasor Diagram of Synchronous Motor

Understanding the phasor diagram of synchronous motors helps in predicting and managing the electrical behavior under different power factor loads.

Example

Generating operation at lagging power factor

We can derive the expression for the Ef by first taking the component of the Vt in the direction of Ia. Component of Vt in the direction of Ia is VtcosΘ, hence the total voltage drop is along the I

 Similarly we can calculate the voltage drop along the direction perpendicular to Ia. The total voltage drop perpendicular to Ia is . With the help of triangle BOD in the first phasor diagram we can write the expression for E

 Generating operation at unity power factor

 Here also we can derive the expression for the E

f by first taking the component of the Vt in the direction of Ia. But in this case the value of theta is zero and hence we have ᴪ = δ. 

With the help of triangle BOD in the second phasor diagram we can directly write the expression for Ef as

Generating operation at leading power factor.

 Component in the direction of Ia is VtcosΘ. As the direction of Ia is same to that of the Vt thus the total voltage drop is .

Similarly we can write expression for the voltage drop along the direction perpendicular to Ia. The total voltage drop comes out to be . With the help of triangle BOD in the first phasor diagram we can write the expression for E